A tin is an area, and most converters scale a width
Going from a 20 cm round to a 23 cm round is not 15 percent more mixture. It is 32. The number on the tin is a width, the mixture fills a floor, and area goes as the square of the width, so the ratio is 23 over 20 squared, which is 1.3225.
Scale by the width and you put about a sixth too little mixture into the tin. That bakes into something thin and dry, and the worst part is that you did a calculation, so you have no reason to suspect the tin.
Going down does the same thing in reverse and is more expensive, because too much mixture in a small tin climbs over the side and burns onto the oven floor.
Four divided by pi
A square tin of side s has an area of s squared. A round tin of diameter s has an area of pi times s squared over four. Divide one by the other and everything cancels except the constant:
4 divided by pi is 1.2732. A square tin holds about 27 percent more than a round tin with the same number printed on it, at every size, because it is a ratio rather than a table.
That is the swap people make most often and check least, usually because the square one is the tin in the cupboard. The same mixture spread over a quarter more floor gives a cake about a quarter shallower, which bakes faster than the recipe says and comes out looking like somebody else's cake.
Scale by the floor, check against the capacity
There are two ratios here and they answer different questions. Using the wrong one is the second most common way to get this wrong.
Floor area is what you multiply the ingredients by. What decides whether a cake cooks properly is how deep the batter is, because heat arrives from the sides and the base and has to reach the middle before the outside gives up. Keep the batter at the depth the recipe intended and everything else about the recipe still holds, including the time.
Capacity tells you whether it will fit. Area times height, and it is the right measure for anything you fill to the brim: a traybake, a pie, a pudding basin, a terrine. It is also the number to check before you pour, because a tin with the right floor and not enough height puts your cake on the oven floor.
A deeper tin of the same width needs no more mixture at all. Same floor, same batter depth, same cake, just more empty air above it. That one surprises people every time.
The bake time goes the opposite way to the mixture
More mixture usually means more minutes, and here it does not, which is why this page gives a direction and a checking instruction rather than a number.
Scale by area and the batter depth does not change. The middle of the cake is no further from any hot surface than it was in the smaller tin, so the recipe time still applies. A much wider tin sets at the edges a little sooner, so start checking early, but the change is small.
What genuinely moves the time is depth. Put a full recipe into a narrower tin and the batter stands taller, the middle is further from everything hot, and it wants longer and about ten degrees cooler so the outside does not finish first. That is a real change and it is the one nobody accounts for, because they were thinking about how much mixture there is.
Water beats geometry for anything with a hole in it
A bundt tin, a ring tin, a fluted brioche mould and a springform with a shaped base have no formula worth writing, because the tube or the flutes remove a share of the volume that varies by tin. Anybody printing a number for "bundt tin" has picked one and hoped.
Fill it with water from a measuring jug and write the number down. That is the tin's real capacity and it took a minute. The measured capacity option on this page takes that figure directly, and it works for any tin, including the ones with perfectly ordinary geometry that turn out to be a centimetre off what the label says.
Measure across the BASE rather than the rim while you are at it. A lot of tins flare outwards, and the base is where the batter actually sits.
Common questions
How do I convert a recipe from a 20cm tin to a 23cm tin?
Multiply the ingredients by 1.32, not by 1.15. The number on a tin is a width and the mixture follows the floor area, which goes as the square of the width: 23 divided by 20 is 1.15, and 1.15 squared is 1.3225. Scaling by the width instead gives you about 15 percent too little mixture, which bakes into a thin dry cake, and the sum looked right on the way in.
Is a 20cm square tin the same as a 20cm round tin?
No, the square holds about 27 percent more. A square of side s has an area of s squared, a circle of diameter s has an area of pi times s squared over four, and dividing one by the other gives 4 over pi, which is 1.2732. Same number printed on both tins, a quarter more cake in one of them. This is the swap people make most often without checking, usually because it is the tin in the cupboard.
Should I scale by area or by volume?
By area for a cake, by volume for anything filled to the brim. What decides whether a cake bakes properly is how deep the batter is, because heat comes in from the sides and the base and has to reach the middle before the outside dries out. Scale by floor area and the batter stays the depth the recipe intended, which is also why the baking time barely changes. Volume is the right measure for a traybake, a pie or a pudding basin, where you fill the thing up.
Does the depth of the tin change how much mixture I need?
Not for a cake, and this surprises people. A deeper tin of the same width has more capacity but the same floor, so the same mixture spread across it sits at exactly the same depth and bakes the same way. Depth decides whether the cake has room to rise without climbing out, which is a different and important question. The tool gives you both figures for that reason.
How much longer do I bake a bigger cake?
Usually barely any longer, if you scaled by area, and that is the counterintuitive part. More mixture spread over more floor at the same depth means the middle is no further from the heat than it was, so the recipe time still roughly applies. What changes the time is DEPTH: squeeze a full recipe into a narrower tin and the batter is deeper, so it wants longer and about 10 degrees cooler or the outside sets before the middle. Nothing here multiplies minutes by a tin ratio, because that number does not exist.
What size tin do I need for a bundt or ring tin?
Fill it with water and measure how much goes in, then use the measured capacity option. A bundt tin has a tube up the middle that removes a share of the volume, and how big a share depends entirely on the tin, so there is no formula worth writing. Water is the ground truth for any tin, and it is the only honest answer for the fluted and shaped ones. Do the same to the tin the recipe asks for if you have it.
Why do American recipes use inch tins?
Because American tins are sold in inches, and the common sizes are 6, 8, 9 and 10 inch, which land at roughly 15, 20, 23 and 25 cm. The 9 inch is the workhorse there in the way the 20 cm is here, so an American recipe moved to a British tin is frequently a step down in size and needs about a quarter less mixture. The table on this page carries both labels for that reason.
Can I bake a cake in a loaf tin instead?
You can, and the shape changes more than the arithmetic suggests. A 2 lb loaf tin has a floor of about 230 square centimetres against 314 for a 20 cm round, so it takes roughly three quarters of the mixture. The bigger difference is that a loaf is narrow and deep, so the batter sits much taller and needs a longer, cooler bake, and the crust on the two long sides forms well before the middle is done. Drop the oven 10 degrees and expect to add time.
What if I only have a bigger tin and do not want more cake?
Bake the recipe as written and accept a shallower cake with a shorter bake, or line part of the tin to make it smaller. A double layer of foil folded into a wall and pressed against the base makes a serviceable divider in a square or rectangular tin. Start checking well before the recipe time, because a thinner layer of the same batter cooks considerably faster, and a sponge that would take 35 minutes at the intended depth can be done in 22.